Which engine in Blender should i start with?
As newbies we started with cycles(side note, we still are newbies).  Cycles looks incredible. It seems to be the most common for achieving photo realistic renders in blender. The draw back is that, it is a little slower. And if set for shorter render times, it can introduce noise. The blender internal render engine is a fast and solid render engine. It can take a little more tweaking to get photorealistic results. In some cases photorealistic results can not be achieved. It has some features that have yet to be ported to cycles or in some cases are just now being imported to cycles, i.e. freestyle, halo and volumetric lighting. The blender can be much faster choice for animations as far as render time. We chose to focus on cycles first and work with the internal render engine as needed.  We have been happy with our choice and results. If you need features from one engine that are missing in the other blender has a compositor at its disposal for combining images. We still have so much to learn. We will be looking into other render engines as well.

Summary:

Cycles Pros


Easier to achieve very photorealistic results


Cycles Cons


Much slower than the internal engine 
Can introduce noise as artifacts


Blender Internal Pros


Much faster than cycles
Has some features that are not present or not as mature in cycles.


Blender Internal Cons


Not as easy to achieve photorealistic results.